The Grappling Hook is an incredibly useful and practical tool, used to grab on to surfaces. It can be used on all solid surfaces and is helpful for navigating caves and building homes as you can use it to cut vegetation.

It does not need to be placed in the hotbar to be used as it has a designated hotkey, (default is E [LT on Xbox]) and, after pressing, the grappling hook will be fired in the direction of the mouse. However, it does have a limited range. It can grab onto a Wood Platform.

You may use other tools at the same time as you are grappled onto a wall, but note that destroying the block you are attached to will break the connection causing you to let go and fall. If connecting to a mud block in mid-air you will keep taking damage.

Grappling hooks can be used to pass through a chokepoint that you would not normally fit through. The endpoint still needs to be at least 3 blocks high and 2 blocks wide, but you can pass though a more narrow gap to get there. As an example, face left in a three block high, horizontal tunnel. Dig the two blocks above your head on the left, and the three to the left of that, starting with your head level, and the two above. You will not be able to jump through that gap, but you can grapple through it.

The grappling hook is an absolute necessity for mining and exploring, and is a massive help as it helps players reach heights and areas otherwise impossible to reach. Players can also use it for quick escapes from water and mobs alike.
As an added perk, by firing the grappling hook at the ground while falling, fall damage can be negated; however, it should be noted that the grappling hook should be fired about 2 seconds before impact, or else the grapple will not hit the block before you do.

Notes

The grappling hook gives you a speed boost if you let go while you are being pulled forward. This can be combined with the Hermes Boots to instantly bring yourself to full speed (including any other speed boosts you might have). When grappled to a closed door, opening the door will fling you forward at a high speed.

If you grapple yourself onto a Door and open it while still attached you will briefly go quickly running past the door in the direction you came from. This also works with Active Stone Blocks, by tethering yourself to one and deactivating it.

The grappling hook lets you go through some small spaces you couldn't go through normally.

You can only attach to the same block for 10 minutes before the grappling hook will automatically detach itself. (8 seconds for mobile)

When using the Grappling Hook or any of its variants (Ivy Whip, Dual Hook, etc.) if you grapple a surface, it will reset Rocket Boots, and Cloud in a Bottle, or any of their variants or improvements, allowing you to use them for full time again.

When grappled to a vertical wall and re-launching the hook while aiming at the wall it will attach to the block above. This can be used for quick and convenient building of walls - just hold down the mouse button and tap the grapple key.

On mobile version the hook can be activated by sliding your finger

Trivia

The tooltip refers to a line that Scorpion, a recurring character in the fighting game Mortal Kombat, shouts just before impaling his opponent with a grappling hook.

You can cancel falling damage with careful use, by firing the Grappling Hook at the ground while falling. This can be done with the Ivy Whip, and Dual Hook too; though with all three it requires good timing. The Dual Hook, like the name says, can fire another hook while the first one is retreating and is thus the easiest, there are mere milliseconds where you're not able to cushion your fall by firing another hook.

If you use a Grappling Hook on the middle part of a closed Door (the second block) and open it, it will send you forward at about the same speed as the pull of the Grappling Hook. Likewise, if you use it on Active Stone Blocks and deactivate them, it will propel you in that direction, so this can be aimed in more directions than just straight forward.

Bugs

When grappling to a 1 block thick wall with water behind it, it will not attach and you will be launched into the air. This does not work in singleplayer.